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Riemann Surfaces
Last Updated: 2026-02-05 16:37:24
Abstract
The course will be a first introduction to Riemann surfaces. These are beautiful objects that sit at the intersection of algebra, geometry, and analysis. We will aim to cover the theorems of Riemann–Hurwitz and Riemann–Roch, as well as the basics of Hurwitz theory. Time permitting, we may delve into additional subjects such as abelian integrals and the Abel–Jacobi theorem.
Objective
The topics presented in the course will include: * Basic facts about Complex Analysis and Manifold Theory * Topology of Riemann surfaces * Meromorphic functions and divisors * Riemann–Roch theorem * Hurwitz theory
Resources
Literature
* E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris. Geometry of Algebraic Curves, Volume 1. Springer-Verlag, 1985 * R. Cavalieri, E. Miles. Riemann Surfaces and Algebraic Curves. Cambridge University Press, 2016 * O. Forster. Lectures on Riemann Surfaces. Springer-Verlag, 1981
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Riemann Surfaces |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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